17-y=1/3y.15+6

Solution for 17-y=1/3y.15+6 equation:

17-y=1/3y.15+6

We move all terms to the left:

17-y-(1/3y.15+6)=0


Domain of the equation: 3y.15+6)!=0

y∈R


We add all the numbers together, and all the variables

-1y-(1/3y.15+6)+17=0

We get rid of parentheses

-1y-1/3y.15-6+17=0

We multiply all the terms by the denominator


-1y*3y.15-6*3y.15+17*3y.15-1=0

Wy multiply elements

-3y^2-18y+51y-1=0

We add all the numbers together, and all the variables

-3y^2+33y-1=0

a = -3; b = 33; c = -1;
Δ = b2-4ac
Δ = 332-4·(-3)·(-1)
Δ = 1077
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{1077}}{2*-3}=\frac{-33-\sqrt{1077}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1077}}{2*-3}=\frac{-33+\sqrt{1077}}{-6}
$